ME
–
210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
Inverse of a Square Matrix
-1
Adj [A]
[A]
=
det A
Adjoint matrix of A
Determinant of A
Adj [A] = [C
ij
]
T
Transpose of the Cofactor Matrix,
[C
ij
]
T
Cofactor Matrix: Matrix formed from cofactors of elements (minors with sign)
Properties of matrix inversion:
[A] [A]
-1
= [A]
-1
[A] = [I]
{[A]
-1
}
-1
= [A]
det{[A]
-1
} = 1 / det[A]
{[A]
T
}
-1
= {[A]
-1
}
T
{[B] [C]}
-1
= [C]
-1
[B]
-1

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